Frequency selective circuits



Jan. 5 1926. 1,568,141

H. W. ELSASSER FREQUENCY SELECTIVE CIRCUITS Filed August 15, 1920 3Sheets-Sheet 1 [1190mm .A arz'o'ua Positive y)? INVENTOR ATTORNEY Jan. 51926. 1,568,141

H. w. ELSASSER FREQUENCY SELECTIVE CIRCUI TS Filed August 13, 1920 3Sheets-Sheet 2 w M m 6' 3V6. c, :EVQ 6 I [p INVENTOR ATTORNEY Jan. 51926.

H. w. ELSASSER FREQUENCY SELECTIVE CIRCUITS Filed August 13, 1920 3Sheet's-Sheet 3 figiljmmel' ATTORNEY mama Jon. 5-, 1m

UNITED STATES ma W. nmsaln, 0! m YORK, 17. Y.,

ABSIGNOB TO AMERICAN Tm AID mnomx comm; a coarom'rron or NEW YORK.

name! mnc'rm moons.

Application filed August 18, 1020. Serial No. 403,367.

To all whom it may cmwern:

Be it known that I, HENRY W. Emassnu, a citizen of the United States,residing at New York, in the county of New York and State of New York,have invented certain Improvements in F1 uency Selective Circuits. ofwhich the fol owing is a specification.

This invention relates to frequency-selective circuits.

It contemplates a network of impedances having a period of seriesresonance and a period of parallel resonance, so that its impedance fora certain frequency of current is very low and for another, very high.

The invention pro ses, further, the use of a. network of this 0 aracterin combination with other impedance elements in a periodic structure ofthe type illustrated and described in the patents to G. A. Campbell,1,227,113 and 1,227,114 of May 22, 1917. Certain new and useful types ofwave filters are thus arrived at, the characteristics of which areexplainedhereinbelow.

This application is related to certain copending cases, Serial Numbers403,368, 403,- 369, 403,370, filed of even date herewith.

A good understanding of the invention may now be had from the followingdescription' of certain specific embodiments thereof, having referenceto the accompanying drawing, in which,

Figure 1 1s a diagrammatic view showing one form of network-embodyingthe invention,

Figs. 2 to 5 inclusive,- are di ammatic views showing varlous types ofters comprising the network of Fig. 1,

Fig. 1 is a graph showing the variation with a frequency in theimpedance of the network of Fig. 1, and

Figs. 2 to 5", inclusive are gra hs showing the variation in attenuationof t e filters of Figs. 2 to 5, respectively.

Similar characters of reference designate similar parts of the severalviews.

The network of Fig. 1 consists of a condenser C in series with a pair ofparallel paths, one of which contains an inductance L, and the other ofwhich a condenser (1,. The impedance of the condenser G, is-

f being the frequency of the current. The

impedance of the parallel resonant path is 10L, 1 wiry-w, (1)

Place for convenience where f, is the frequency at which L and C, areresonant. Substitute equation 2 in equation 1 and simplify. Then whereThe expression in the brackets of the above equation may be placed equalto K. Then where The variation in the value of K with frequency is shownby the curves of Fig. 1*, in which the valuesof K are ordinates and theratios of to' f, are abscissee. These curves indicate the manner inwhich the impedance of the network changes with frequency, as may beseen by an inspection of equation 4. At low frequencies the impedance ofthe network is negative, but as the frequency is raised, the impedancechanges from negative to positive, the point of crossing of the axis ofabscissae denoting series resonance of C and the combination of G, and Lor zero impedance of the network. The impedance then increases until, atthe frequency at which L, and O, are in arallel resonance its value isinfinite. The impedance t on chan s sign and thereafter decreases,Tapproac ing zero at infinite frequency. 6

network, therefore, has two periods of reso- 11o nance, a period ofseries resonance at one frequency and a period of parallel resonance ata higher fre uency. The period of parallel resonance depends on therelative value 6 of only two impedance elements, namely L and O and theperiod of series resonance is governed by the values of all threereactances. The curves of Fig 1 are drawn for an ideal networkcontaining no resistance or other dissipative elements, but in an actualcase, the resistance may be made so small that its efiect is practicallynegligible. It thus a pears that the network of Fig. 1 may e used as aselective circuit for passing current of series resonant frequency andpreventing the passage of current of parallel resonant frequency.

I have found, moreover that by employing the network as a shunt andseries impedance in a periodic structure like that discussed in theCampbell patents hereinbefore mentioned, certain new types of wavefilters are arrived at, which filters have certain new and valuablecharacteristics which I shall 95 now describe.

Figs. 2, 3, 4 and illustrate four types of filters employing the networkof Fig. 1, the first two of these views showing the network as a shuntimpedance element and the last two as a series impedance element of thefilter section. Figs. 2 and 3 show an inductive and a capacityreactance, respectively as the series impedance element, and Figs. a and5 show the same reactances, respectively, as the shunt impedanceelement.

The properties of the above filters may be determined from certainmathematical expressions which set forth the relations existing betweenthe frequency of current and the impedance elements of the filters. Inthe Campbell patents hereinbefore mentioned, it was shown (equation 2)that for a periodic structure of the type now under consideration, inwhich the series impedance per section is Z and the shunt impedance persection is Z the attenuation per section of the filter may be derivedfrom the relation cosh '=1/2 +1 (6) naeem in which denotes thepropagation constant of t e structure. The variation of the attenuationof any filter with frequency of current may, therefore, be deduced fromequation 6, when the corresponding values of Z and Z are substitutedtherein. For the filter shown in Fig. 2, the value of Z, is

2 is a graph showing the variation of the attenuation of the filter ofFig. 2, as computed from equation 9. The axis of the abscissae is laidofi in ratios of f to f and the axis of the ordinates in values of theattenuation constant per filter section. An inspec-- tion of the curvesshows that the attenuation is nil for two ranges of frequencies, f, tof, and f, to f,. The filter, in other words,passses Without attenuation,only such frequencies as lie below 7, or between f and f,. It is,therefore, a combined low-pass and band filter and performs thefunctions of both. It is characterized, moreover, by having infinite g5attenuation at a frequency f which is close to f,, and it discriminates,consequently, with particular sharpness against frequencies just abovethe upper limit of the lowpass range.

The frequencies f f and f, may be evaluated as follows: it was shown inthe said Campbell patents, that for unattenuated transmission, must be apure imaginary, and that, therefore, the value of cosh must lie between*1. The frequencies which limit the ranges of free transmission mayconsequently be determined by placing equation 9 equal to +1 and 1respectively, and solving for 7. When this is done, it will be foundthat the roots are respectively,

Lee a z L202 4 4) 16 214 C;

is infinite, may be evaluated by placing nation 9 equal to co andsolving f,

.WODOQ i 1 -r m/ The attenuation characteristics of the remainingfilters may be arrived at in a similar manner, The curves of Fig. 3

show that the filter of Fig. 3 passes without substantial attenuationonly a single band, the limiting values of-which are 1 and f The filteris further characterized. y having infinite attenuation per section at afreuency f below f This frequency may be 'c osen within the lowerattenuated range, but preferably so as to lie close to f ,.so

' that the filter has a sharp cut-ofi at the lower limit of thetransmitted band.

The frequencies f f,,, and f... may be evaluated similarly as thelimiting frequencies'of the filter of Fig. 2. The expression for cosh inthe present case is, since Z is acapacity reactanoe,

cosh P a/2 m 14 By placing equation 14 e ual res tively to' +1 and -1,simplifying, and solving for f, the roots will be found to be i which issimilar to equation9 exce t that 1 Tm When nation 14 is placed equal toco and solved or f, the frequency of maximum attenuation, f.,,, is foundto be derived from the expression.

cosh f" 1/2 the value of Z and Z are interc anged, the shunt impedanceof Fig. 2 being the series im ance of Fig. 4, and vice, versa. Thelimltin frequencies are obtained, as before, by p acing cosh equal to +1i pd -1 respectively and solvlng for f.

enoe

1' 1 fI- T +6 The expression for the frequency of maxiinum attenuation,f is obtained by placing c lsfih equal to on and solving for f.

. 1 r 22 mitt The curves of Fig. 5 show that the filter of Fig. 5 is ofthe single band type and similar to that of Fig. 3, difiering therefrom,however, in that the frequency of infinite attenuation lies in the u perattenuated range. This filter, may caused to have a sharp cut-ofi at theupper limit of the band. The attenuation curve of Fig. 5 is derived fromthe expression,

and the values of f and f and f are obtained by placing the aboveexpression for cosh equal to +1 and 1 and co, respectively:

It should be noted that the attenuation curves herein illustrated referto the ideal structure in which the resistance of the im pedance unitsis zero. In a practical filter there is a departure from these curves,owing to energy dissipation. In any case, however, the resistance may bemadeso small that the departure from the ideal .is practicallynegligible.

The formulae 1013, 15-17, 19-22, and 2e25, given above, may be used indesigning filters to meet any specified sets of conditions. Since thereare four independent impedance elements in each filter section,

any four properties of the filter dependent upon the values of theimpedance elements but independent of each other may be chosen at will.For example, in the design of a filter of the type illustrated in Fig.2, two of. the design conditions may be taken as the frequencies f, andf and the third as f thus defining the ranges of free transmission. Thisleaves one condition open to choice, and this may be taken as theimpedance of the filter at any desired frequency, or as the value of anyone of the elements of the filter section. In the design of a filter ofthe type of Fig. 3, two of the design conditions may be chosen as thefrequencies f and f and the third as 7%,, thus wearer leaving the fourthto be chosen in accordance with any other condition that may prevail.Similar considerations apply to the remaining types of filters.

As an example of the application of the formulae, let it be re uired todesign a filter of the type illustrate in Fig. 3, which shall transmitfrequencies between 4:00 and 2500 cycles, and which shall have maximum,ideally infinite, attenuation at 360 cycles, so that it has aparticularly sharp out-ofi at the lower limit of the freely transmittedrange. Frequencies f f and f are thus specified as 400, 2500 and 360cycles respectively. As a fourth design factor let it be assumed thatcertain considerations dictate that the value of L shall be .5 henry.Applying formula (16), we find that 0 1100810 microfarads. Substitutingin (17) we have hence hence Therefore C =.398 microfarads.

All the constants of the filter are thus determined. It will readily beseen that, instead of-the above-mentioned set of conditions, any othersinvolving 'the filter impedances may be imposed, it being understoodthat the above example is merely a simple illustration, and in no waylimits the invention.

Although only certain forms of filters embodying the invention are shownand de-' scribed herein, it is readily understood that various changesand modifications may be made therein within the scope of the followingclaims, without departing from the spirit and scope of the invention.

What is claimed is: H

1. A wave filter of the type having like recurrent sections and in whicheach section consists of a series element and a shunt element, one ofthese elements consisting of a capacity reactance in series with aplurality of paths in parallel with each other, one of said pathscomprising inductive reactance and the other of said paths comprisingcapacity reactance.

2. A wave filter of the type having like recurrent sections and in whicheach section consists of a series element and a shunt element, one ofthese elements consisting of a reactance in series with a plurality ofpaths in parallel with each other, one of said paths comprisinginductive reactance and the other of said paths comprising capacityreactance.

3. A filter for an electric circuit, consisting of an impedance inseries with the circult and an impedance in shunt thereto, one of saidimpedances consistin of a single reactance element and the ot er of anetwork comprising a capacity reactance in series with a pair ofparallel paths, one of which consists of a capacity reactance and theother of an inductive reactance.

4. A filter for an electric circuit consisting of an impedance in serieswith the circuit and an impedance in shunt thereto, one of saidimpedances consisting of a single reactance element and the other of anetwork comprising a reactance in series with a pair of parallel paths,one of which consists of a capacity reactance and the other of aninductive reactance. k

5. The method of discriminating among alternating current componentsaccording to their frequency which consists in passing currents offrequency from zero to a certain finite frequency, then attenuatingcurrents of higher frequency1 up to another certain finite frequency wita maximum of attenuation close to the lower of these two frequencies,and then passing currents whose frequency ranges from the upper limitingfrequency previously mentioned to a thir 10 frequency still higher andattenuating all currents of frequency higher than the last mentioned fuency.

6. A wave ter of the type having like recurrent sections and having aseries ele- 6 ment and a shunt element in each section, 'said filterembodying means in said elements to provide two separate ranges offrequencies for free transmission, one lying between finite boundinfrequencies and the other bounded by a i nite frequency and extendingthence over the whole remaining frequency range on that side.

7. A wave filter of the type having like recurrent sections and having aseries element and a shunt element in each section,

said filter embodying means in said elements to provide two separateranges of frequencies for free transmission, one lying between finiteboundin frequencies and the other range lyin be ow the first mentionedrange and exten ing between a finite frequency and zero.

8. A filter of recurrent sections having 1 four reactances in eachsection and iving two free transmission bands, one band having bounds atfinite frequencies, the other extending from another finite frequencybound over the whole frequency range on that side, the values of thereactances being determined as functions of the said three finitebounding frequencies and of the characteristic impedance of the filterat the extreme of the free transmission range for which there is only asingle finite frequency bound.

In testimony whereof, I have signed my name to this specification this10th day of August, 1920.

HENRY w. ELSASSER.

